To add to what the previous posters have said, your Counter TI may also play a part. Your team will still occasionally counter without it, what it does is it decreases the threshold for them to attempt one.
Now, counterattacks are high-risk/high-reward plays, that can result in high-quality chances but more often than not result in lost possession, often leading to a counter opportunity for the opposition when the turnover finds 8-9 of your players committed in their third.
The trade off might be worth it if you are the inferior team and chances are hard to come by, but the more you dominate the game, the less worth it it becomes.
Think about it this way. Say counter gains you 4-5 quality entries in the final third over the course of the match. But due to it's risky nature, the turnover also gives the opposition 2-3 counter opportunities.
Now, when from open play your team already has 20 such chances, that's only a 20-25% increase, whereas the defending team who might otherwise have 2-3 chances from regular play, gets an 100% increase.
TLDR: it's not to say you don't gain anything from the Counter TI, but depending on the circumstances the opposition may gain more, relatively speaking.

The DLF dropping deep will generally create space for himself between the lines, but whereas in real life the opposition defender will sometimes choose shadow the DLF to deny him that space, that pretty much never happens in FM. That's not to say a DLF is ineffective, it's one of my favorite roles and he still pulls defenders out of position to an extent when they try to close him down after he has already received the ball.

If you have the pace, and Man Utd does, the TI can certainly be useful against teams who play a high d-line or push up their fullbacks. I'd say your left IW and AF are in a good position to exploit those spaces.

That's a fair point, it's definitely affecting the whole team, what I was questioning is to what degree can an improvement of that magnitude can be put down to the TI's synergy with the tactic or that role in particular and to what degree on other factors - squad quality, form, opposition tactics, variance.
My guess is that opposition tactics also played a big part, the OP mentions both were inferior teams so there's a good chance both were set up defensively, sat deep and pressed little so there was little space available to exploit.
To me instructions like Pass Into Space or Run At Defence/Dribble Less are rather situational and not core elements of a tactic.

Could have something to do with it, in that if your DLF lacks pace he cannot contest balls into space and he'd be better off receiving the ball at his feet.
But I still think it's mostly due to randomness, I doubt that instruction has that big of an effect on the performance of any one player.

I for one am in the camp that the game already gives us players too much info as it is, but I agree that the info the UI gives us on player personalities is too scarce.
From a design point of view, I assume the attributes and descriptions are intended to represent the manager's own perception - watching the players in matches, in training or just interacting with them as people, as well as third party accounts of these things.
Judging other people is what we all do instinctively at all times and humans in general are surprisingly good at reading other humans.
Now, it doesn't have to be as granular as the 1-20 values attributes are, but it's strange that our manager personnas cannot perceive anything more than a short description of the personality of someone they are presumably working with daily. This is just something that's universal, be it right or wrong, justified or not, I for one can sure find more than one word to describe the people I interact with regularly.
There's the legal aspect here of course, having the game slapping unambitious or unprofessional tags left and right would quickly get SI in hot water, but even so a compromise can be reached by only emphasizing the positive traits - not too dissimilar in this regard to how balanced personality is used now.
Of course, my argument holds true for our own players, there should be a thick fog of war over most players, except perhaps the highest reputation ones. It's part of the general criticism I have of the game, that there isn't enough asymmetry in what we know about our own players and team, and what we know about the rest of the game world.

The ones that the game highlights are a good place to start but you need to keep in mind that those hold true for the standard settings.
Depending on your team and player instructions, the key attributes for each role will naturally change.
Then, some roles are more flexible than others, a BBM as long as he's got good stamina and workrate, can work out with any number of player moulds.

From my experience the chances stat is unreliable and I don't pay much attention to it.
For me as well the shots pattern is the most important thing to look at, not just their location as in inside vs outside the box, but also wide vs central, number of blocked shots, how many of them are at the end of a cross or which players are taking them.

The point I was arguing wasn't that aggression was the culprit, but rather pressing settings that are too high.
Your players prioritize pressuring the ball carrier and leave their positions as a result.
Things like formation or OIs can play a part here as well.

Stay back if needed is an excellent set piece role for when you don't want to get taken by surprise by the opposition leaving 3 players forward for a corner. But when they do not, this player is on simple "go forward" instructions, which may not fit the active routine at all.
My suggestion is to turn this role from a primary set pieces role to a checkbox we can turn on for any role.
What roles are a essential depends from routine to routine and this would give us flexibility, sometimes I may want the player attacking the far post staying back if needed, other times it's the one lurking outside the area.

If I understood jumping reach correctly, the value is normalized for all heights, in that a 5ft5 player with 11 jumping will jump just as high as a 6ft5 player with 11 jumping.
That doesn't mean height is not an advantage, because players will not always be able to jump, such as when turning or during a physical duel, and in those instances a player's height is what dictates aerial reach.
Furthermore, I'm speculating here, but a shorter player even if he can jump a certain height, he may need to exert more effort to do that so his balance, strength or heading accuracy may suffer.